clicking noise under dash and hot air.
The HVAC system has ‘blend doors’, these control blending the hot and cold air, and the direction of the airflow, I.e. floor, dash, or defrost. The clicking is the actuator for the blend door.
You could try googling it to see if it is something you wish to try doing yourself. I had mine fixed about 6 months ago but can not recall how much it was.
The blend doors are usually driven by electric servo motors driving plastic gears. If some of the teeth break off the gear, the motor keeps running trying to get the door into the proper position.
Taking apart a dash to repair these usually is a very expensive operation.
There are two types of control doors in your HVAC system
These are the blend door and mode doors.
The blend door controls if cold or hot air enters the cabin.
The mode doors control where this cold/hot air comes out of the HVAC system.
There’s a problem with the blend door/actuator.
Concur, probably a problem with a blend door actuator. But ask at a dealership if a blend door homing procedure might be the best first course of action.